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Chapter 2: Q 31 (page 155)

Find a function f that has the given derivative f' and value f(c).

f'x=8e4x+1,f0=3

Short Answer

Expert verified

The anti derivative isf(x)=2e4x+x+1

Step by step solution

01

Step 1:Given informatiom

Given expression isf'(x)=8e4x+1,f0=3

02

Step 2:Simplification

Given f'(x)=8e4x+1

We will use an intelligent guess-and-check method to find f

here e4xis derivative of e4x4

Therefore for 8e4xantiderivative is 2e4x

And 1 is derivative of x

Hence

width="127" height="23" role="math">f(x)=2e4x+x+c

Now,

f0=3鈬�3=2e0+0+c鈬�3=2+c鈬�c=1

therefore,

f(x)=2e4x+x+1

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